Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

ECON 2101

MICROECONOMICS 2

T1 2023

Written Questions 1

Deadline: 5 pm, Friday 17 March, 2023

Question 1:  9 Marks

Ashwin likes to spend her spare time in summer in one of two ways:

(i) watching cricket (x) at Sydney Cricket Ground or

(ii) watching movies (y) at Ritz cinema.

In choosing how to entertain herself, she considers both constraints---money and time.

Part I (3 marks)

Ashwin has 48 hours of spare time in a month. A cricket game runs for 8 hours, while each visit to the movies takes up 4 hours. Each month, Ashwin also has $324 to spend on entertainment. A ticket for a cricket game costs $45. A visit to the movie costs $36.

(a) (1 mark) Write down Ashwin’s budget constraint and time constraint.

(b) (2 marks) Draw Ashwin’s budget constraint and time constraint in a clearly labelled diagram. Label all axis intercepts in the two axes (x and y) and the point of intersection of the two budget lines. Shade the set of bundles that Ashwin can afford (those satisfying both his time and money constraints) with vertical lines.

Part II (3 marks)

Sam---a friend of Ashwin---has the same amount of spare time (48 hours per month) and same amount of money to spend on entertainment ($324 per month). He faces the same constraints as Ashwin. However, Ashwin and Sam have slightly different preferences over cricket (x) and movies (y).

· Sam’s utility function: U(x,y) = x + y

· Ashwin’s utility function: V(x,y) = min{x,y}

Each maximizes their own utility.

a) What is/are the utility maximizing bundle/s for Sam?

b) What is/are the utility maximizing bundles for Ashwin?

Part III (3 marks)

To attract cricket fans back after Covid as well as to cover revenue shortfall, the local cricket association has decided to offer a season ticket for $144. Tickets are now NO LONGER sold separately for each game (i.e., the season ticket is the only option if one wants to watch cricket at SCG). With the season ticket Ashwin can watch as many cricket games as he wants.

(c) (1 mark) Draw Ashwin’s new budget constraint for money, and shade in his new affordable set of bundles with horizontal lines.

(d) (2 marks) Is Sam better off or worse off with the introduction of season ticket? What about Ashwin?  

Question 2: 8 marks (1, 1, 1, 2, 3)

Deborah’s utility over consumption (C), hours worked (H), and hours spent in commute (S) is:

(1) U (C, H) = C^1/2 – H – S.

The maximum number of hours that Deborah can work productively is 10. Thus

(2) 0 ≤ H ≤ 10.

On the days which Deborah works, she spends 2 hours in commuting from home to work and then back (one hour each way).

(3) If H > 0, S = 2. Else if H = 0, S = 0.

Assume that  and . For simplicity, we also assume that there are no other costs (e.g., ticket costs, parking fee) associated with commuting.

(a) (1 mark) Explain why Deborah’s preferences are not strongly monotone in C and H. Use an example to support your answer.

(b) (1 mark) Deborah’s marginal utility from consumption (C) is strictly decreasing in C. True or False? Explain.

(c) (1 mark) Draw an indifference curve in (H, C) space that yields U = 6. Make sure to plot hours worked (H) in horizontal axis and (C) in vertical axis and label at least two points/bundles which give U = 6.

(d) (2 marks) Deborah’s income is hourly wage (w) times the hours worked (H).  Suppose w = $32 per hour and price of C is $1. How many hours would Deborah work to maximize her utility? How much C will Deborah choose? Assume that Deborah has no other sources of income.

(e) (3 marks) Deborah has received a new job offer which pays $w* an hour. However, it requires relocation closer to city where prices are at least 30% higher. More concretely, price of C is $1.30 instead of $1. On the plus side, relocation will cut down Deborah’s commuting time from 2 hours per day to 30 minutes per day (15 minutes each way). That is, S will decline from S = 2 to S = 0.5.

Deborah is a utility maximizer. Deborah will accept the offer if and only if w* > _________.

Fill in the blank. Explain your answer.

Question 3 9 marks (3, 3, 3)

A consumer has the following utility function

U (x₁, x₂) = (x₁ + 3) (x₂ + 4)

Prices of the two goods x₁ and x₂ respectively are p₁ and p₂ and the consumer has income m. We assume that all prices and income are strictly positive. Furthermore, throughout this question we assume that m is high enough so that both goods are consumed in strictly positive amount in equilibrium.

(a) (3 marks) Solve the consumer’s optimization problem and express the demand for the two goods in terms of prices and income. 

(i) (3 marks) Compute the missing values of elasticities in the following table assuming M = 10, p₁ = 2, and p₂ = 1. Show your work. 

(b) (3 marks) While x₂ is produced locally, x₁ is transported from a different region. Assume p₂ = 1.  Building a new railroad (that connects the regions) will reduce transportation cost which in turn will reduce the price of good 1 from p₁ = 2 to p₁ = 1. Railroad will be funded by taxes which will reduce each consumer’s disposable income from m = 10 to m = 10 – T. A utility-maximizing consumer will accept higher taxes as long as

T ≤ _____________.